Letters to a Young Mathematician
by Ian Stewart
Clever Proof That Math Has Its Charms
A review by Paul A. Robinson Jr.
Is it possible to trisect an angle using only a straight edge and a compass? This
is not the central point of Ian Stewart's Letters to a Young Mathematician,
but it is one of the curious threads woven into these delightful letters written
to "Meg," a fictitious mentee, as she advances through a career in mathematics.
Stewart begins by framing and discussing the questions that most non-mathematicians
ask. "What is mathematics? Hasn't it all been done? What do mathematicians
do?" If this was all this book did it would simply follow in the wake of
G.H. Hardy's elegant 1940 memoir A
But fortunately, Stewart, who is a professor of mathematics at the University
of Warwick in England, goes beyond that in these letters that follow Meg in
roughly chronological order, from high school to a tenured position at a university.
Each chapter addresses one or two questions, beginning with "Why study
mathematics?" and concluding with speculations on the nature of God. In
the process, Stewart not only provides insight into the life of an academic,
but also cleverly introduces the names of the greats of the math world, in addition
to offering a booklist (from science fiction to biography) for the well read.
It's a brilliant way to help the reader develop fondness for the pursuit of
mathematics without resorting to actual mathematical theorem and proof (although
theorems are discussed as well).
Stewart hints, for instance, at the marvelous story of Wiles proving Fermat's
last theorem. He tantalizes us with clever problems such as trisecting an angle.
He evokes "the inner beauty of mathematics ... its ideas, the generalities,
the sudden flashes of insight," but does so without taking the reader through
To the mathematician, as Stewart explains, nature is one grand excuse for mathematics,
"the development of mathematics is, and always has been, a two-way trade
between real-world problems and symbolic or geometric methods devised to obtain
answers. Of course math is effective for understanding nature; that, ultimately,
is where it comes from."
So subjects like "bird crystals" - how birds arrange themselves on
phone lines - and groupoids - "natural algebra's structure that replaces
the symmetry group" - pop up in delightful ways. Stewart's illustrations
are drawn from a variety of problems that demonstrate what mathematicians do
and how they think, even as it taps into their excitement over both process
For nonmathematicians, Letters to a Young Mathematician offers wonderful
insight into academics, a reading list in a variety of fields, and a bit of
knowledge about Gauss, Fibonacci, Leibniz, Feynman, and Fermat. It also serves
as a primer on mathematicians, their culture, their tribal customs, and their
community. For mathematicians themselves, Stewart provides first-rate career
advice and offers a charming example of how best to talk to the rest of us.
Paul A. Robinson Jr. is a professor of physics at Principia College
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